Young's and shear moduli and Poisson's ratio of La0.6Sr0.4Co0.2Fe0.8O3-d (LSCF6428), La0.6Sr0.4CoO3-d (LSC), and La0.6Sr0.4FeO3-d (LSF) were investigated in the temperature range from room temperature to 1173 K and in the oxygen partial pressure, P(O2), range from 1 x 10-1 to 1 x 10-4 bar by the resonance method. The Young's and the shear moduli decreased with increasing temperature at low temperatures and drastically increased at intermediate temperatures. The drastic increase was associated with the second-order phase transition. In contrast, the Poisson's ratios of LSCF6428, LSC, and LSF decreased around the phase transition temperature. The P(O2) dependence of the Young's and the shear moduli of LSCF6428 showed different tendencies depending on temperature. At 873 K, the Young's and the shear moduli were almost independent of P(O2), whereas they increased with decreasing P(O2) at 973 K. At 1073 K, they first increased with decreasing P(O2) under higher P(O2) and then gradually decreased under lower P(O2). At 1173 K, they monotonically decreased with decreasing P(O2). Such complicated P(O2) dependence were interpreted by complex influences of the phase transition, the chemical expansion and the variation of the oxygen nonstoichiometry and the cation mean valence.